What is dedendum?

Short Answer:

Dedendum is the portion of a gear tooth that lies below the pitch circle. It is the radial distance between the pitch circle and the bottom of the tooth space, known as the dedendum circle. The dedendum provides space for the addendum of the mating gear during meshing.

In simple terms, it represents the depth of the tooth below the pitch circle. The dedendum is slightly greater than the addendum to provide clearance between mating gears and prevent interference or contact between the bottom of one tooth and the tip of another.

Detailed Explanation :

Dedendum

Dedendum is an essential parameter in the geometry of gears. It represents the depth or the lower portion of a gear tooth that extends from the pitch circle down to the root circle (the bottom of the space between two adjacent teeth). The dedendum ensures there is enough space for the top part (addendum) of the mating gear tooth to engage properly during motion. It allows smooth transmission of power and helps to prevent jamming between gear teeth.

In simple words, the dedendum is the part of the tooth below the pitch circle that provides clearance for the meshing gear. The correct value of dedendum ensures proper fitting, smooth motion, and reduced wear in gears.

Definition and Meaning

Dedendum can be defined as:
“The radial distance between the pitch circle and the bottom of the tooth space is called the dedendum.”

The dedendum circle, also called the root circle, passes through the bottom of the gear teeth. This circle is smaller than the pitch circle and defines the minimum diameter of the gear. The dedendum portion of a gear tooth ensures that the top of one gear’s tooth (the addendum of the mating gear) can move freely into the space of the other gear without causing friction or collision.

In standard gear design, the dedendum is slightly greater than the addendum to provide necessary clearance. For a standard full-depth involute system, the dedendum is generally given as:

This extra 0.25m provides clearance between mating gears to avoid interference.

Purpose of Dedendum

The main purpose of the dedendum is to provide space for the mating gear’s addendum during engagement. This space ensures smooth and continuous motion without interference.

Some key roles of the dedendum are:

  1. To provide clearance: The dedendum allows enough gap for the top of the mating tooth to move freely.
  2. To prevent interference: Proper dedendum prevents the tip of one gear’s tooth from hitting the root of another.
  3. To ensure smooth motion: The dedendum ensures proper meshing, reducing vibration, noise, and uneven wear.
  4. To maintain proper gear ratio: Correct dedendum helps maintain accurate speed ratio by ensuring proper tooth contact.
  5. To improve gear life: Adequate dedendum reduces stress on teeth and prevents early failure.

Dedendum Circle

The dedendum circle or root circle is the imaginary circle that passes through the bottom of the gear tooth spaces. It represents the smallest diameter of the gear. The diameter of this circle can be calculated using the formula:

This circle defines the limit up to which the teeth are cut below the pitch line. It is critical in ensuring correct clearance and meshing between gears.

Importance in Gear Design

Dedendum plays a vital role in the strength, operation, and durability of gears. The following points explain its importance in detail:

  1. Smooth Engagement:
    The dedendum ensures that the gear teeth engage and disengage smoothly without sudden shocks or slipping.
  2. Proper Clearance:
    The slight increase in dedendum compared to addendum provides clearance between the tooth tip of one gear and the root of the other.
  3. Load Distribution:
    Adequate dedendum helps distribute load uniformly across the gear teeth, reducing the chances of wear or tooth breakage.
  4. Avoids Interference:
    Improper dedendum can lead to interference, causing mechanical noise, friction, and possible damage to the gear.
  5. Standardization and Interchangeability:
    Since dedendum is related to the module, gears with the same module can mesh properly even if they are from different manufacturers.

Standard Values

In standard gear systems, the dedendum value depends on the gear type and standard followed. For involute spur gears,

  • Addendum = 1 × module (m)
  • Dedendum = 1.25 × module (m)

This extra 0.25m ensures clearance between mating gears. In stub tooth gears, the dedendum is reduced, typically 1.0m, because the teeth are shorter and thicker.

Example Calculation

Suppose a gear has a module (m) of 4 mm and a pitch circle diameter of 100 mm.
Then,

The dedendum circle diameter can be found as:

Thus, the dedendum circle is 90 mm in diameter, representing the lowest part of the gear tooth profile.

Relationship between Addendum and Dedendum

The addendum and dedendum together define the total depth of the gear tooth.

For a standard full-depth system,

This relationship ensures that the teeth have proper height for engagement and clearance.

Conclusion

Dedendum is the distance between the pitch circle and the root of the gear tooth. It represents the lower portion of the tooth and provides the required clearance for proper meshing with the mating gear. The dedendum is slightly greater than the addendum, typically equal to 1.25 times the module, to prevent interference and ensure smooth power transmission. It plays a major role in gear efficiency, wear reduction, and durability. A correctly designed dedendum ensures smooth, quiet, and reliable gear operation.